Judge, facing Boston reliever Addison Reed, struck out swinging, bringing him to 0-for-4 on the day. The Red Sox won 5-1.
Judge has 167 strikeouts this season, the third-most in a single season in Yankees history and the second-most in the majors this season; the Twins' Miguel Sano leads the majors with 170 strikeouts.
Girardi said he's still got faith in the presumptive AL Rookie of the Year, adding, "It's not like we have a lot of people that are hitting very well."
Said Judge: "It's a little frustrating, but there's nothing you can do about it. You can't pout. You can't cry. You just have to keep working and move on."
On Saturday, Judge broke the record previously set by Montreal Expos pitcher Bill Stoneman in 1971, for the longest strikeout streak in a single season by any player.
The rookie's 37 straight games with a strikeout is also tied for the longest streak over two seasons. Stoneman struck out in 37 straight games spanning the 1971 and '72 seasons.
Judge struck out three times in Saturday's game, marking his 13th game this season with three K's, tied with Curtis Granderson in 2012 for the most in a single season by a Yankees player since 1920.
Judge has struck out in all 15 games he has played against the Red Sox this season; he is hitting .155 and has only one home run against Boston.
The Associated Press contributed to this report.